Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
832 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26021917 | C2 | semidirect |
| 2. #26020636 | C2 | semidirect |
| 10. Q82×C89 | C4 | semidirect |
| 12. #555×C89 | C4 | semidirect |
| 130. C89 | #12773 | semidirect |
| 132. Q82 | Dic89 | semidirect |
| 134. #555 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021917 | 2 |
| #26020636 | 2 |
| C89×#3483 | 2 |
| #12773 | 89 |